Question

Express the interval
(−2, 6) in terms of an inequality involving absolute value. (Use the variable x to describe the interval.)

Answer 1

Find the center of the interval.

Answer 2

i have no idea how to do this

Answer 3

Did you do what I said?

Answer 4

whats the center 4?

Answer 5

Why would that be the center? It's not +2, it's -2. You MUST pay better attention.

Answer 6

-2+6=4?

Answer 7

-2-6 = -8

Answer 8

That's the sum. That's not the average or center of two values.

Answer 9

Find the center of the interval. You can just walk ir off if you like.

-2 6
One step each way
-1 5
0 4
1 3
2 2 <== There it is!

Answer 10

how will i express that with absolute value?

Answer 11

How far is the center from the two endpoints?

Answer 12

(0,4)?

Answer 13

Why would it be an interval? We need an absolute distance.

How far is 2 from 6?
How far is 2 from -2?

Answer 14

4 and 2

Answer 15

The difficulty with what I am dragging you through is that we are BUILDING the solution. You cannot see the end from where we are. I hope to show you a PROCESS, not an answer.

Where is the center of the interval? (6 - (-2))/2 = 2
How far is each endpoint from the center? 6-2 = 4 and -2 - (-2) = 4

This is how absolute values work. It is sometimes called "magnitude" or "absolute distance" or "norm" and maybe a few other things. In any case, it is a positive number referring to how far apart things are.

Our task here is the describe the set of all numbers that are less than 4 from 2. How do we do that?

Answer 16

2<x<4?

Answer 17

You're just guessing and you failed to use an absolute value.

4 is the ONLY distance that matters.
2 is the ONLY center of the interval that matters.

Give it another go.

Hint: It will have only one inequality.

Answer 18

|x|+2<4

Answer 19

Now THAT was a good effort. |x-2| < 4

Read this, everything that is less than 4 away from 2.

Answer 20

Thanks alot for the help.. I really appreciate it!